Test Drive accident. Dealer asking me to pay

Hey everyone, I need some advice regarding a test drive incident today. I got a call drom mandovi showroom in Mysore to test drive a Maruti Fronx. They came to my home with the car to test. While driving on a narrow road, an oncoming vehicle forced me to swerve slightly within my lane, and unfortunately, I hit a rock that was in the middle of the road. The front tyre burst, and it was an alloy wheel. The showroom representative immediately started insisting that I either: 1. Book the car 2. Pay ₹6000 for the tyre 3. Get a new tyre through a dealer he knows (Note. This was not a red number plate unit.) I explained that this was an accident, I was driving carefully and below the speed limit, and I hadn’t driven recklessly. I also asked him to email me the details about why the insurance wouldn’t cover the damage, but he refused. When he called his manager, the manager also refused to provide anything in writing and instead kept saying, "Why should we do anything official when you hit the rock unofficially?" which sounded really suspicious to me. They pressured me for a while, and when I tried calling the NEXA helpline, they only forwarded me back to the same dealer's manager. Eventually, since it was getting late, we agreed that I would return to the showroom tomorrow to discuss further. I didn’t sign anything, didn’t give them my driving license, so I think I’m safe in that regard. But I’m still worried. Are they allowed to demand payment for tyre damage during a test drive? Shouldn’t this be covered under insurance? Has anyone faced a similar situation before? What should I do when I go back tomorrow? Or should I even go back? Any legal or practical advice would be greatly appreciated!